I had a situation similar to this a few years ago. What my hunting partner and I ended up doing was placing a few trail cameras in the trees with an angle to catch the vehicles license plate while coming and going. In addition to this, we took some 1/2" plywood and put 1 3/4" screws through it. We placed 1' x 1' strips of this in each of the tire tracks on the inside of the gate (which had no trespassing signs on it). We buried the plywood under some dead grass and a little bit of dirt. If you din't know they were there, you would never know you ran over them.
After about a week, we went back to check and sure enough the trail cameras had a -CENSORED--CENSORED--CENSORED--CENSORED--CENSORED--CENSORED- off trespasser on them. Also, showed a tow truck coming to his rescue. I'm assuming that all 4 of his tires went flat. Also, the lease was about 90mi from the closet town, so we can only guess what his towing bill was.
We made a police report and notified the local GW and Sheriff. Since then, we haven't had any issues with trespassers.